Question

Which of the following not a factor of 3x² + 6x-45

A (x + 5)
B (x - 3)
C (x-4)
D 3
Please explain how to do each step so I will know how to do it for the rest of the other problems that has the same problem, but with different numbers.

Answer 1

C, (x-4) is not a factor
give me a moment to explain

Answer 2

first there is a factor of 3 that goes throughout the equation
take out the 3 from 3x^2 + 6x - 45 to get
3( x^2 + 2x - 15)
a way you can tell automatically that 3 had to be one is that each of the other terms has an x in it and your initial equation only went to x^2 so only 2 terms could have an x in it

next look at the equation you got after taking the 3 out:
x^2 + 2x - 15, you know the foil method to multiply monomials eg ( x-3)(x+5)
to reverse this look at the last term and the middle term. the last term is what the two numbers multiplied will be and the middle is the 2 added
look at (x-3)(x+5); the -15 comes from them being multiplied, the +2 comes from them being added

Answer 3

Factor out a 3 from each of your terms first. \[3(x^{2}+2x-15)\]

Next, find the factors of -15 that have a difference of +2, the coefficient of your middle term. The factors of -15 which add to +2 are -3 and +5. So, this leads to

3(x-3)(x+5) as the factors of your polynomial.

Answer 4

now How did you get 3(x-3) (x-5)?

Answer 5

it's like taking the equation apart piece by piece. you took the 3 out so that becomes the
3(x^2 +2 - 15)
then you took apart the x^2 +2x-15 to (x-3)(x+5)
so if x^2+2x - 15 = (x-3)(x+5) you can just substitute that into the first equation here to have
3(x-3)(x+5)
the process of taking a binomial apart just takes practice

Answer 6

The 3 comes from the common factor in all three terms, and as both David and I have explained, David in more detail, is that when you have a trinomial whose leading coefficient of 1, you just have to find factors of the constant at the end which add to the coefficient of the middle term.

Answer 7

What happens to the 2 though?

Answer 8

3x^2 +6x -45
all three of these has a common multiple of 3:
i. 3*1 = 3
ii. 3*2 = 6
iii. 3* -15 = -45
so when you take out the 3 you have to divide each term by 3 so:
3x^2 + 6x - 45 become 3( 1x^2 + 2x - 15)

Answer 9

the 2 is accounted for when using the foil method
(x - 3)(x+5)
foil is
First, Outer, Inner, Last
First:
x*x = x^2
Outer:
x*5 = 5x
Inner:
-3*x = -3x
Last:
-3*5 = -15
Add them all together to get
x^2 + 5x - 3x - 15 ; then you simplify the x terms
5x - 3x = 2x ; so you have
x^2 + 2x - 15

Answer 10

I'm starting to get it. THank you! Very helpful. ^.^